System and method for real-time rendering of complex data

ABSTRACT

Methods for volume rendering of 3D object data are provided. The methods can include classifying 3D object data and determining a transfer function to use to render the 3D object data based on the classification; incrementally determining voxels to render from the 3D object data; and/or determining a grid that represents the voxels and rendering based on the voxel grid.

FIELD OF THE INVENTION

The invention relates generally to rendering data on a computer. Morespecifically, the invention relates to rendering three-dimensional (3D)objects on a two-dimensional (2D) display, virtual reality and/oraugmented reality.

BACKGROUND OF THE INVENTION

Currently, three-dimensional (“3D”) objects can be rendered. Currentsystems can allow for visualizing 3D objects obtained with, for example,imaging devices, other systems and/or inputs. Currently, 3D objects canbe processed for 3D printing, visualized on a two-dimensional (“2D”)screen, and/or visualized in augmented and/or virtual reality.

Current 3D objects can provide vital information for medicalprofessionals. For example, for a doctor performing heart surgery on aneonate, visualizing the heart of the neonate, rather than a genericneonate heart model, can be the difference between a successful andunsuccessful surgery. It can be desirable to visualize via a computerscreen (e.g., two-dimensional (“2D”) screen), via virtual reality, viaaugmented reality and/or by 3D printing a model of the neonate.

Current systems for visualizing 3D objects can be limited. For example,although 3D objects can be presented to a user (e.g., doctor), it can bea presentation that typically does render the 3D object with sufficientspeed to avoid delay when zooming or rotating the object. The delay canbe so long that it can make usage of these current systems unrealizable.For example, a doctor may want to visualize the 3D object with thepatient looking on. In another example, a doctor may want to review the3D object with another doctor. In these scenarios, the duration it takescurrent systems to render volumes may prevent the doctor from utilizingthese current system in scenarios where real-time processing can be moreimportant. For example, current methods for rendering a CT image with100 slices can have a rendering rate of 2 frames/second. Virtual realitycan require rendering at 90 frames/second.

Separately, current systems can suffer from an inability to render the3D object with a high level of resolution such that small details (e.g.,blood vessels of a heart) of an object can be understood when viewed.One difficulty with accuracy can include differentiating betweendifferent parts of a 3D object. For example, when rendering a 3D objectthat includes tissue, current rendering techniques typically cannotdistinguish between soft tissue and blood vessels. Thus, both parts aretypically rendered having the same color. Therefore, it can be desirableto volume render 3D objects with sufficient speed and/or accuracy suchthat the rendering is usable.

SUMMARY OF THE INVENTION

One advantage of the invention is that it can provide an increasedrendering speed and/or a reduction in an amount of data duringvisualization and/or 3D printing, by for example, providing methods thatcan be faster and/or can require less computations then known methods.

Another advantage of the invention is that it can provide a moreaccurate representation of 3D objects, showing for example, smalldetails of an object with a high level of fidelity. Another advantage ofthe invention is that it can provide faster zooming, rotating, meshcreation, mask creation, data modification, and addition and/or removalof segments of the 3D object when visualized. Another advantage of theinvention is that it can allow for improved distinguishing between partsof an object.

According to embodiments of the present invention, there is providedmethods for volume rendering three-dimensional (3D) image data, andnon-transient computer readable mediums containing program instructionsfor causing the methods.

According to embodiments of the present invention, one method caninclude determining a material classification for each voxel in the 3Dimaging data; determining a corresponding transfer function for eachmaterial classification; and rendering each voxel in the 3D imaging databased on a transfer function that corresponds to the materialclassification corresponding to the voxel. Determining the correspondingtransfer function may be further based on a HU value.

In some embodiments of the present invention, the determination of thematerial classification can further include: determining an initialmaterial classification; segmenting the 3D imaging data; and determiningthe material classification based on the initial material classificationand the segmented 3D imaging data. Determining an initial materialclassification value may be based on a HU value of the respective voxel,a probability map, or any combination thereof.

In some embodiments of the invention, the segmenting is based on amagnitude of a gradient of each voxel. Segmenting the 3D imaging datamay further include determining an intersection between the segmented 3Dimaging data.

According to embodiments of the present invention, another method couldinclude: performing a first raycasting on a 3D object to produce a firstintermediary frame, performing a second raycasting on the 3D object toproduce a second intermediary frame, and mixing the first intermediaryframe and the second intermediary frame to render the 3D object.

The first raycasting can have a first position and a first step size,and the second raycasting can have a second start position and a secondstep size. The first start position and the second position can bedifferent, and the first step size and the second step size can bedifferent. The first step size can be based on the sampling rate of therecasting. The second step size can be based on the first step size andan offset.

In some embodiments of the invention, the second start position can bethe first start position with an offset value. The offset value can berandomly generated, input by a user, or any combination thereof.

In some embodiments of the invention, mixing the first intermediaryframe values and the second intermediary frame values can furtherinclude, for each pixel that is in the same pixel location in the firstintermediary frame and the second intermediary frame, mixing the firstintermediary frame values and the second intermediary frame values atthe pixel location to determine final pixel values at the pixellocation.

In some embodiments of the invention, mixing the first intermediaryframe values and the second intermediary frame values can furtherinclude averaging the first intermediary frame values and the secondintermediary frame value, performing a weighted averaging of the firstintermediary frame values and the second intermediary frame values,accumulated averaging, or any combination thereof.

According to embodiments of the present invention, another method couldinclude generating a voxel grid based on the 3D object. Each voxel inthe voxel grid can have a three dimensional location, a sizespecification, and voxel values. Each voxel in the voxel grid canrepresent a center point of a 3D cube volume having the respective sizespecification. The size specification can be input by a user, based on atype of the 3D object, size of the 3D object of any combination thereof.

For each voxel in the voxel grid, whether the 3D cube volume is emptycan be determined. If the 3D cube volume is empty, an empty value can beassigned to the current voxel in the voxel grid. If the 3D cube volumeis not empty, a present value can be assigned to the current voxel inthe voxel grid. For each voxel in the voxel grid having a present value,the corresponding 3D cube volume based on the corresponding 3D objectcan be rendered to a frame for display on the 3D screen.

In some embodiments, the method involves rendering the voxel grid basedon the present and empty values to a frame for display on the 3D screen.The rendering can be performed on a graphical processing unit.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting examples of embodiments of the disclosure are describedbelow with reference to figures attached hereto that are listedfollowing this paragraph. Identical features that appear in more thanone figure are generally labeled with a same label in all the figures inwhich they appear. A label labeling an icon representing a given featureof an embodiment of the disclosure in a figure can be used to referencethe given feature. Dimensions of features shown in the figures arechosen for convenience and clarity of presentation and are notnecessarily shown to scale.

The subject matter regarded as the invention is particularly pointed outand distinctly claimed in the concluding portion of the specification.The invention, however, both as to the organization and the method ofoperation, together with objects, features and advantages thereof, canbest be understood by reference to the following detailed descriptionwhen read with the accompanied drawings. Embodiments of the inventionare illustrated by way of example and are not limited to the figures ofthe accompanying drawings, in which like reference numerals indicatecorresponding, analogous or similar elements, and in which:

FIG. 1 shows a block diagram of a computing system for volume rendering,according to an illustrative embodiment of the invention;

FIG. 2 shows a flowchart of a method for rendering 3D objects, accordingto an illustrative embodiment of the invention;

FIG. 3 shows a table that can be used with the method of FIG. 2,according to an illustrative embodiment of the invention;

FIG. 4 shows a flowchart of a method for rendering 3D objects, accordingto an illustrative embodiment of the invention;

FIG. 5 shows a flowchart of a method for rendering 3D objects, accordingto an illustrative embodiment of the invention; and

FIG. 6 shows screenshots of a volume, an optimized tree and a frame,according to some embodiments of the invention.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn accuratelyor to scale. For example, the dimensions of some of the elements can beexaggerated relative to other elements for clarity, or several physicalcomponents can be included in one functional block or element. Further,where considered appropriate, reference numerals can be repeated amongthe figures to indicate corresponding or analogous elements.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However, it will be understood by those skilled in the art that theinvention can be practiced without these specific details. In otherinstances, well-known methods, procedures, and components, modules,units and/or circuits have not been described in detail so as not toobscure the invention. Some features or elements described with respectto one embodiment can be combined with features or elements describedwith respect to other embodiments. For the sake of clarity, discussionof same or similar features or elements cannot be repeated.

Although embodiments of the invention are not limited in this regard,discussions utilizing terms such as, for example, “processing,”“computing,” “calculating,” “determining,” “establishing”, “analyzing”,“checking”, or the like, can refer to operation(s) and/or process(es) ofa computer, a computing platform, a computing system, or otherelectronic computing device, that manipulates and/or transforms datarepresented as physical (e.g., electronic) quantities within thecomputer's registers and/or memories into other data similarlyrepresented as physical quantities within the computer's registersand/or memories or other information non-transitory storage medium thatcan store instructions to perform operations and/or processes. Althoughembodiments of the invention are not limited in this regard, the terms“plurality” and “a plurality” as used herein can include, for example,“multiple” or “two or more”. The terms “plurality” or “a plurality” canbe used throughout the specification to describe two or more components,devices, elements, units, parameters, or the like. The term set whenused herein can include one or more items. Unless explicitly stated, themethod embodiments described herein are not constrained to a particularorder or sequence. Additionally, some of the described methodembodiments or elements thereof can occur or be performedsimultaneously, at the same point in time, or concurrently.

FIG. 1 shows a block diagram of a computing system for volume rendering,according to an illustrative embodiment of the invention. Computingsystem 100 can include a controller 105 that can be, for example, agraphical processing unit (GPU) and/or a central processing unitprocessor (CPU), a chip or any suitable computing or computationaldevice, an operating system 115, a memory 120, executable code 125, astorage system 130, input devices 135 and output devices 140.

Controller 105 (or one or more controllers or processors, possiblyacross multiple units or devices) can carry out methods describedherein, and/or execute the various modules, units.

Operating system 115 can include any code segment (e.g., one similar toexecutable code 125 described herein) that can perform tasks involvingcoordination, scheduling, arbitration, supervising, controlling or othermanaging operation of computing system 100, for example, schedulingexecution of software programs or executable code segments, or enablingsoftware programs or other modules or units to communicate. Operatingsystem 115 can be a commercial operating system.

Memory 120 can be a Random Access Memory (RAM), a read only memory(ROM), a Dynamic RAM (DRAM), a Synchronous DRAM (SD-RAM), a double datarate (DDR) memory chip, a Flash memory, a volatile memory, anon-volatile memory, a cache memory, a buffer, a short term memory unit,a long term memory unit, or other suitable memory units or storageunits, or any combination thereof. Memory 120 can be or can include aplurality of memory units. Memory 120 can be a computer or processornon-transitory readable medium, or a computer non-transitory storagemedium, e.g., a RAM.

Executable code 125 can be any executable code, e.g., an application, aprogram, a process, task or script. Executable code 125 can be executedby controller 105 possibly under control of operating system 115. Forexample, executable code 125 can be an application that renders a 3Dobjects onto a 2D screen or produces instructions for printing a 3Dobject by a 3D printer as further described herein. Although, for thesake of clarity, a single item of executable code 125 is shown in FIG.1, a system according to some embodiments of the invention can include aplurality of executable code segments similar to executable code 125that can be loaded into memory 120 and cause controller 105 to carry outmethods described herein. For example, units or modules described hereincan be, or can include, controller 105, memory 120 and executable code125.

Storage system 130 can be or can include, for example, a hard diskdrive, a Compact Disk (CD) drive, a CD-Recordable (CD-R) drive, aBlu-ray disk (BD), a universal serial bus (USB) device or other suitableremovable and/or fixed storage unit. Content can be stored in storagesystem 130 and can be loaded from storage system 130 into memory 120where it can be processed by controller 105. As shown, storage system130 can store 3D objects (e.g., imaging data 131), mask data 132,rendering data 133, a transfer function data 134, voxel grid data 136,and/or a material ID list 137. The 3D object can include any data thatis representative of a 3D object. The 3D objects can include 3D imagingdata, mesh data, volumetric objects, polygon mesh objects, point clouds,functional representations of 3D objects, cad files, 3D pdf files, STLfiles, and/or any inputs that can represent a 3D object. The 3D imagingdata can include medical imaging data, including Computed Tomography(“CT”) imaging data, a Cone Beam Computed Tomography (“CBCT”) imagingdata, a Magnetic Resonance Imaging (“MRI”) imaging data and/or MRAimaging data (e.g., MRI with a contrast agent) or ultrasound imagingdata. The 3D objects can be of anatomy (e.g., complex anatomy),industrial data, or any 3D object.

Data stored in storage system 130 is further described herein. As isapparent to one of ordinary skill in the art, the storage system 130 andeach dataset therein, can all be in one storage system or distributedinto multiple storage systems, in various configurations.

In some embodiments, some of the components shown in FIG. 1 can beomitted. For example, memory 120 can be a non-volatile memory having thestorage capacity of storage system 130. Accordingly, although shown as aseparate component, storage system 130 can be embedded or included inmemory 120.

Input devices 135 can be or can include a mouse, a keyboard, a touchscreen or pad or any suitable input device. It will be recognized thatany suitable number of input devices can be operatively connected tocomputing system 100 as shown by block 135. Output devices 140 caninclude one or more screens, displays or monitors, speakers and/or anyother suitable output devices. It will be recognized that any suitablenumber of output devices can be operatively connected to computingsystem 100 as shown by block 140.

Any applicable input/output (I/O) devices can be connected to computingsystem 100 as shown by blocks 135 and 140. For example, a wired orwireless network interface card (NIC), a printer, a universal serial bus(USB) device or external hard drive can be included in input devices 135and/or output devices 140.

A system according to some embodiments of the invention can includecomponents such as, but not limited to, a plurality of centralprocessing units (CPU) or any other suitable multi-purpose or specificprocessors or controllers (e.g., controllers similar to controller 105),a plurality of input units, a plurality of output units, a plurality ofmemory units, and a plurality of storage units. A system canadditionally include other suitable hardware components and/or softwarecomponents. In some embodiments, a system can include or can be, forexample, a personal computer, a desktop computer, a laptop computer, aworkstation, a server computer, a network device, or any other suitablecomputing device. For example, a system as described herein can includeone or more devices such as computing system 100.

Imaging data 131 can be any imaging data as known in the art, e.g.,imaging data 131 can be medical data such as produced by a CT system orby an MRI system and/or by a CBCT system.

A mask included in masks 132 can correspond to object types. Forexample, for an object of a heart, the masks can be the right ventricle,the left ventricle, a right aorta, a left aorta. For a cellphone, themasks can be keys, buttons, wires, computer chips, screens, etc. A maskmay be, for example, a data construct including, for example, Boolean(e.g., I/O, yes/no) values for each voxel or data point in a larger dataset. A mask may include visual markers (e.g., color and/or patterns)that specify appearance of the voxel. The mask when applied to thelarger data set may indicate that a voxel is marked or is not marked.

In some embodiments, input of a 3D object (e.g., an organ such as a heador heart) is received. The system can retrieve from memory a set ofmasks that correspond to a type of the object. The system can populateeach mask in the set of masks with the corresponding 3D object data. Forexample, an imaging data of a heart, a left chamber mask and a rightchamber mask can be retrieved from memory. A portion of the imaging datathat corresponds to the right chamber of the heart can be assigned tothe right chamber mask and the portion of the imaging data thatcorresponds to the left chamber mask can be assigned to the left chambermask.

Operations performed on masks can include operations performed onvoxels, e.g., eroding, dilating, expanding or shrinking voxel sizes andso on. It will be understood that masks, meshes and voxels can be, orcan be represented or described by, digital objects as known in the art,accordingly, any morphological or logical operations can be performedfor or on masks, meshes and voxels and described herein. For example,dilating a voxel can include changing one or more values of the voxel,e.g., size, location and so on.

For example, using morphological or logical operations, a group A ofvoxels can be dilated with spherical element of radius R (denoted hereinas “A⊕R”), a group A of voxels can be eroded with spherical element ofradius R (denoted herein as “A⊖R”), a group A of voxels can be openedwith spherical element of radius R (denoted herein as “A⊚R”) and a groupA of voxels can be closed with spherical element of radius R (denotedherein as “A⊙R”).

The system can render the set of masks having assigned imaging data intoa format that can be displayed on a 2D screen, displayed in virtualreality, displayed in augmented reality and/or 3D printed. For example,based on imaging data received from a CT or an MRI system and based on aset of masks, some embodiments can produce frames for displaying a 3Dobject on a 2D screen.

Rendering data 133 can be any data usable for rendering an image or forprinting a 3D object. For example, rendering data 133 can be a set ofpixel values (e.g., RGBA and HU values, hue, intensity and so on) thatcan be used to render or print an image or object as known in the artand/or rendering data 133 can be a set of instructions that can be usedto cause a 3D printer to print an object as known in the art.

Transfer function 134 can be any function or logic. For example,transfer function 134 can be a function or logic that receives a set ofinput values (e.g., a HU value and a material identification) andproduces as output a description of a pixel, e.g., RGBA values, locationor offset of the pixel and the like. For example, transfer function 134can include a set of transformation tables for a respective set oforgans, e.g., a first transformation table for a heart, a secondtransformation table for a bone, and each transformation table canassociate HU values with pixel descriptions as described.

Voxel grid 136 can be a set of voxels that represents a space or volume.For example, a voxel grid can be a set of voxels that represents a spacecontaining a 3D organ or system, e.g., voxels in a voxel grid can cover,include, or occupy the space that includes a 3D representation of ablood vessel or system, a head and the like. Any number of voxel gridscan be used, for example, a first voxel grid can cover an entire object,organ or space, a second voxel grid can cover or relate to bones, athird voxel grid can describe, include, cover or be otherwise related toblood vessels and so on.

Material identification (ID) list 137 can be any list, table orconstruct that maps or links a set of values to a respective set ofmaterials. For example, material ID list 137 can map HU values tomaterials, e.g., as shown by table 310 in FIG. 3.

A mesh (or polygon mesh or triangle mesh as known in the art) can be aset of vertices, edges and faces that define or describe a 3D object. Asknown in the art, a mesh can be used for conversion into a format for 3Dprinting.

During volume rendering, it can be desirable to render a volume thatdistinguishes between parts of a 3D imaging data. For example,distinguishing between bone and a bed a patient lies upon duringimaging.

In one aspect, the invention can involve determining a transfer functionfrom a set of transfer functions for each voxel in the 3D imaging databased on a material classification index. Varying the transfer functionamong voxels within the 3D imaging data can allow for high qualityimages that have clarity, by for example, selecting a transfer functionthat corresponds to a particular part of an object being rendered.

FIG. 2 is flowchart of a method for volume rendering, according to anillustrative embodiment of the invention. The method involvesdetermining a material classification for each voxels in a 3D imagingdata (Step 210). The material classification can be determined based oneor more attribute values of the voxel. For example, the materialclassification can be determined based on the HU attribute as follows: avoxel with the HU value in the range of −2048 to −600 can be assigned amaterial classification of air, a voxel with a HU value that is in therange of 200 to 450 can be assigned a material classification of bone.

In some embodiments, the material classification is determined by i)performing an initial material classification of the voxels in the 3Dimaging data, ii) segmenting the voxels in the 3D imaging data, and/oriii) performing a final material classification of the segmented voxelsin the 3D imaging data.

i. Performing an Initial Material Classification

The initial classification can vary based on the type of 3D imaging data(e.g., CT imaging data, CBCT imaging data, or MRA (MR plus contrastagent) imaging data).

For CT imaging data, the initial material classification can be based onthe HU attribute. For example, FIG. 3 shows an example of table 310 thatcan be used to determine an initial material classification. As shown bytable 310, the HU ranges can correspond to material type. As is apparentto one of ordinary skill in the art, table 310 is an example only, andHU values can be assigned to different material types.

For CBCT imaging data, the initial material classification can be basedon results of a bias field estimation. The bias field estimation can bedetermined as shown in M. N. Ahmed et. al. “A Modified Fuzzy C-MeansAlgorithm for Bias Field estimation and Segmentation of MRI Data” 2002,IEEE Transactions on medical imaging, incorporated herein by referencein its entirety, with the following as example inputs:expected means,σ=0.5, ε=10⁻⁵, σ=1, p=2. The expected means can be determined bydetermining a Gaussian Mixture Model of 6 Gaussians with means U_(i).The expected means of each material can be determined by a maximizationupon voxels in the range of [−500, 3000] The expected means can be setto [U₁, . . . U₆, −1000]. An output of the bias field estimation canrepresent the bias field and a set of probability 3D Volumes P_(i) foreach material. A Best Probability Map (BPM) can be determined based onthe index i of the maximal probability for each voxel. The initialmaterial classification can be based on the BPM values. For example,voxels with a BPM value of 7 can be initially classified as “Air”;voxels with BPM values of 1, 2, 3 can be initially classified as “SoftTissue”; voxels with BPM value of 4, 5, 6 can be initially classified as“Bone.”

For MRA imaging data, the initial material classification can be basedon the bias field estimation, e.g., as described above with respect toCBCT imaging data, with the following as example inputs: expected means,σ=1, ε=10⁻⁵, σ=1, p=2. The expected means can be determined bydetermining a Gaussian Mixture Model of 5 Gaussians with means U₁. Theexpected means of each material can be calculated based on a smoothedand/or filtered MRA imaging data.

For example, the MRA imaging data can be smoothed and/or a backgroundthreshold can be determined. The MRA imaging data can be smoothed via aGaussian smoothing method with σ=1. The background threshold can bedetermined as shown in EQN. 1 and 2, as follows:

NoDataThreshold=0.02*max_(HU)(Smoothed MRA imaging data)  EQN. 1

modified MRA imaging data=[1>NoDataThreshold]  EQN. 2

The expected means can be set to [U₁, . . . U₅]. The BPM can bedetermined based on the output of the bias field estimation. The initialmaterial classification for the MRA imaging data can be based on the BPMvalues. For example, voxels with a BPM value of 1 can be initiallyclassified as “Air”; all voxels not classified as air can be classifiedas “body”; voxels at the perimeter of the “body” can be classified as“skin”; voxels with a BPM value of 2, that are classified as “body” andnot classified as “skin” can be classified as “soft tissue”; voxels witha BPM value of 3 that are classified as “body” and not classified as“skin” can be classified as “muscle”; voxels with a BPM value above 4that are classified as “body” and not classified as “skin” areclassified as “vasculature”; remaining voxels are classified as “noise”.

ii. Segmenting the Voxels

The 3D imaging data voxels can be segmented based on the initialmaterial classification index. For example, assume that the materialclassification is bone, vasculature, and muscle. Each voxel in the 3Dimaging data having a material classification of bone can be segmentedinto a first segment, each voxel in the 3D imaging data having amaterial classification of vasculature can be segmented into a secondsegment, and each voxel in the 3D imaging data having a materialclassification of muscle can be segmented into a third segment.

In some embodiments, the segmentation can further involve dilating,eroding, opening and/or closing initially segmented voxels. In someembodiments, the segmentation can vary based on the type of 3D imagingdata (e.g., CT imaging data, CBCT imaging data, or MRA imaging data).

In some embodiments, the CT imaging data can be segmented into vessels,bones, muscle, and/or low contrast vasculature. For a vessel segment(“VesselSegment”), the segmentation can be determined as follows:

-   -   a. Voxels that are initially classified as “Bone” or        “Vasculature” can be segmented into a general segment        (“GeneralSegment”);    -   b. Voxels that are initially classified as “Dense Bone” or        “Teeth” can be segmented into possibly metal segment        (“PossibleMetalSegment”);    -   c. Voxels that are initially classified as “Vasculature” can be        intermittently into a low vessel segment (“LowVesselSegment”);    -   d. VesselSegment=GeneralSegment∪(|∇g|<150):        -   The magnitude of the gradient |∇g| can be determined as            shown in EQN. 3 through 6, as follows:

$\begin{matrix}{{G_{x}\left( {x^{\prime},y^{\prime},z^{\prime}} \right)} = {\frac{\delta \; I}{\delta \; x} = \frac{{I\left( {{x^{\prime} + 1},y^{\prime},z^{\prime}} \right)} - {I\left( {x^{\prime},y^{\prime},z^{\prime}} \right)}}{2}}} & {{EQN}.\mspace{14mu} 3} \\{{G_{y}\left( {x^{\prime},y^{\prime},z^{\prime}} \right)} = {\frac{\delta \; I}{\delta \; y} = \frac{{I\left( {x^{\prime},{y^{\prime} + 1},z^{\prime}} \right)} - {I\left( {x^{\prime},y^{\prime},z^{\prime}} \right)}}{2}}} & {{EQN}.\mspace{14mu} 4} \\{{G_{z}\left( {x^{\prime},y^{\prime},z^{\prime}} \right)} = {\frac{\delta \; I}{\delta \; z} = \frac{{I\left( {x^{\prime},y^{\prime},{z^{\prime} + 1}} \right)} - {I\left( {x^{\prime},y^{\prime},z^{\prime}} \right)}}{2}}} & {{EQN}.\mspace{14mu} 5} \\{{\nabla g} = \left\lbrack {G_{x},G_{y},G_{z}} \right\rbrack} & {{EQN}.\mspace{14mu} 6}\end{matrix}$

-   -   -   where x′, y′ and z′ are coordinates of the current voxel for            which the material classification index is being determined.            A magnitude of the gradient can be determined as shown in            EQN. 7, as follows:

|∇g|=√{square root over (G _(x) ² +G _(y) ² +G _(z) ²)}  EQN.7

-   -   e. PossibleMetalSegment=PossibleMetalSegment⊕3;    -   f.        VesselSegment=VesselSegment∪(PossibleMetalSegment∩GeneralSegment)—e.g.,        step “f” can remove images of a stent or other metal elements        around vessels;    -   g. LowVesselSegment=(LowVesselSegment⊙1)⊚3—e.g., step “g” can        connect small vessels to each other, the opening operation can        remove noise caused by muscle tissue;    -   h. VesselSegment=((VesselSegment∪LowVesselSegment)⊚1)⊙2—e.g.,        step “v” can connect small vessels to the large vessels in        VesselSegment, and can remove noise from bone tissues around the        vessels;    -   i. Remove all connected components that are under 1000 voxels        from VesselSegment—e.g., to eliminate noise that is, for        example, characterized, or caused, by small connected        components; and    -   j. VesselSegment=VesselSegment⊙4—e.g., VesselSegment can include        vessel tissues or boundaries of soft tissue.

A bone segment (“BoneSegment”) can be determined as follows:

-   -   a. Voxels that are initially classified as “Bone” or “Dense        Bone” or “Teeth” can be segmented into true bone segment        (“TrueBoneSegment”);    -   b. Remove connected components below 50 voxels from the        TrueBoneSegment—e.g., step “b” can reduce calcifications that        were classified as bone;    -   c. TrueBoneSegment=TrueBoneSegment⊕4—e.g., can ensure that        TrueBoneSegment covers an area surrounding dense bone tissue;    -   d. PossibleBoneSegment=GeneralSegment∩¬VesselSegment;    -   e. Remove from PossibleBoneSegment every connected component        that does not touch TrueBoneSegment by 100 voxels to obtain        BoneSegment—e.g., step “e” can connect the soft bone tissue        voxels to the dense bone tissue voxels.

A muscle segment (“MuscleSegment”) can be determined as follows:

-   -   a. Voxels that are initially classified as “Muscle” can be        segmented into MuscleSegment;    -   b. Voxels that are initially classified as “Vasculature” can be        segmented into a low contrast Segment “(LowContrastSegment”).

In some embodiments, certain voxels segmented as “Vasculature” or “Bone”are improperly segmented, as they can be of another object (e.g., anobject with an HU>100). In some embodiments, voxels can be segmented as“Bed” or “Skin,” as follows:

-   -   a. Voxels with HU above −150 can be segmented into a relevant        segment (“RelevantSegment”);    -   b. A largest connected component in RelevantSegment can be        segmented into an object segment (“ObjectSegment”);    -   c. ObjectSegment=ObjectSegment⊕2—e.g., step “c” can fill holes        in ObjectSegment, ObjectSegment can describe the objects body in        the scene, with its close surroundings;    -   d. BedSegment=[HU>—500]∩¬ObjectSegment;    -   e. SkinSegment=((ObjectSegment⊖1)∩¬(ObjectSegment⊕3))⊕2

In some embodiments, the CBCT imaging data can be segmented into skinand/or noise. A CBCT skin segment (“SkinSegment”) and a noise segment(“NoiseSegment”) can be determined as follows:

-   -   a. A minimal HU the CBCT 3D imaging data can be marked as        (“MinHUVal”).    -   b. A probable object segment (“ProbableObjectSegment) can be        determined: ProbableObjectSegment=([HU>−500]⊙1)⊚1;    -   c. An object segment (“ObjectSegment”) can be determined by        region growing ProbableObjectSegment with a standard deviation        (e.g., 10), bounding the HU values to be between [−600,−500];    -   d. A relaxed object segment (“ObjectSegmentRelaxed”) can be the        result of region growing ProbableObjectSegment with HU values of        [−700,−500] and standard deviation of 10;    -   e.        ObjectSegment=(ObjectSegment⊙5)∪(ObjectSegmentRelaxed⊙5)—e.g.,        step “e” can fill holes in ObjectSegment;    -   f. NoiseSegment=[HU>−500]∩¬ObjectSegment;    -   g. SkinSegment=(ObjectSegment⊕1)∩¬(ObjectSegment e 1);    -   h. A DICOM scene segment (“DicomSceneSegment”) can be        determined: DicomSceneSegment=[HU>MinHUVal]    -   i. DicomSceneSegment=DicomSceneSegment⊚3—e.g., step “i” can fill        holes in the DicomSceneSegment;    -   j. Remove the last 50 rows in DicomSceneMask—e.g., Step “j” can        be required due to the fact that most scans are in shape of a        tube, thus the back parts of the skull can be neglected;    -   k. SkinSegment=(SkinSegment∩DicomSceneSegment)⊕2;    -   l. NoiseSegment=NoiseSegment∩¬SkinSegment.

iii. Performing a Final Material Classification

A final material classification can be determined. In some embodiments,the 3D imaging data can have a final material classification that isequal to the initial material classification.

The 3D imaging data can be finally materially classified based on thesegmentation.

In various embodiments, for CT imaging data, voxels belonging to(GeneralSegment∩¬VesselSegment∩PossibleBoneSegment) can be finallymaterially classified as “Dense Bone”; voxels belonging to(GeneralSegment∩(VesselSegment∩(¬VesselSegment U ¬PossibleBoneSegment)))can be finally materially classified as “Vasculature”; voxels belongingto (TrueBoneSegment∩(MuscleMsak∪LowContrastSegment)) can be classifiedas “Bone/Vasculature”; voxels belonging to(¬TrueBoneSegment∩¬MuscleSegment∩(MuscleMsak∪LowContrastSegment)) can befinally materially classified as “Noise.”

In some embodiments, voxels that have an initial material classificationof “Fat” are removed using the open operation with 1 voxel radius of the“Fat” voxels. The removed voxels can be finally materially classified as“Noise.”

In various embodiments, voxels in SkinSegment can be finally materiallyclassified as “Skin” and/or voxels in “BedSegment” can be finallymaterially classified as “Bed.”

In various embodiments, for CBCT imaging data, voxels belong toNoiseSegment are finally materially classified as “Noise” andSkinSegment can be finally materially classified as “Skin.”

In some embodiments, voxels of MRA imaging data are finally materiallyclassified according to their initial material classification.

Various corrections or modifications of voxels material classificationscan be made. For example, there might be voxels with HU values that arefar from their initial threshold (e.g., due to the operations asdescribed above) which can be misclassified. To correct suchmisclassifications, an embodiment can perform some or all of thefollowing steps:

-   -   a. “Fat” voxels with HU above −20 are classified as Vasculature;    -   b.“Fat” voxels that are neighbors to a bone tissue voxel are        classified as “Bone”;    -   c. “Muscle” voxels that have HU above 390 are classified as        Bone/Vasculature;    -   d.“Skin” voxels with HU above 10 are classified as Muscle.

Determining the material classification index for CT imaging data canalso involve determining a maximal dimension of the input CT imagingdata (e.g., the maximal width/length/depth) and, if the maximaldimension is above a threshold value, the CT imaging data can be scalede.g., to a predefined dimension

The method can also involve determining a transfer function (e.g.,transfer function 134, as described above in FIG. 1) for each materialclassification (Step 215). For example, if the material classification(e.g., indicates a bone) of a first voxel of the 3D imaging data isdifferent than the material classification (e.g., value indicates atissue) of a second voxel, then the first voxel can be rendered using afirst transfer function, and the second voxel can be rendered using asecond transfer function. The first transfer function and the secondtransfer function can be different.

The transfer function can be determined by selecting one transferfunction from a set of transfer functions. The set of transfer functionscan be stored in memory and/or input by a user. The set of transferfunctions can be based on desired color for a particular object type.For example, vessels are typically red, and bone is typically white.Therefore, the transfer function can include a smooth transfer of colorsbetween red and white. As is apparent to one of ordinary skill, thistransfer function and colors discussed are for example purposes only. Insome embodiments, the transfer functions can be constant for differentHU/grayscale values (e.g., for CBCT and/or MRA). Table 1 shows anexamples of transfer functions based on classification and HU value, asfollows:

TABLE 1 Classification HU Value RGB Value Air −2048 and −600 (0, 150,150) Skin Fat −2048 and −600 (255, 70, 30) Skin Fat 400 and −61 (255,70, 30) Skin Fat −60 and 0 Smoothly transferring between (255, 70, 30)to (134, 6, 6) Skin Fat 1 and 100 Smoothly transferring between (134, 6,6) to (251, 135, 115) Skin Fat 101 and 500 Smoothly transferring between(251, 135, 115) to (247, 170, 119) Skin Fat above 501 (247, 170, 119)Skin −2048 and −61 (255, 70, 30) Skin −60 and 20 Smoothly transferringbetween (255, 70, 30)to (65, 0, 00) Skin above 20 (65, 0, 0) Fat −2048and −61 (255, 120, 17) Fat −60 and 200 Smoothly transferring between(255, 120, 17) to (65, 0, 0) Fat 200 and 800 Smoothly transferringbetween (65, 0, 0) to (251, 135, 115) Fat above 800 (251, 135, 115)Muscle −2048 and 100 (65, 0, 0) Muscle 101 and 800 Smoothly transferringbetween (65, 0, 0) to (251, 135, 115) Muscle above 800 (251, 135, 115)Muscle/Vessel −2048 and 199 (134, 6, 6) Muscle/Vessel 200 and 800Smoothly transferring between (134, 6, 6) to (251, 135, 115)Muscle/Vessel above 800 (251, 135, 115) Vessel −2048 and 300 (134, 6, 6)Vessel 200 and 800 Smoothly transferring between (134, 6, 6) to (251,135, 115) Vessel above 800 (251, 135, 115) Bone/Vessel −2048 and 0 (134,6, 6) Bone/Vessel 0 and 150 Smoothly transferring between (134, 6, 6) to(251, 135, 115) Bone/Vessel 151 and 400 Smoothly transferring between(251, 135, 115) to (247, 170, 119) Bone/Vessel above 400 (247, 170, 119)Bone Boundary −2048 and 0 (247, 170, 119) Bone Boundary 0 and 150Smoothly transferring between (247, 170, 119) to (205, 205, 205) BoneBoundary above 150 (205, 205, 205) Strong Bone All (255, 255, 255) TeethAll (255, 255, 255) Vessel Noise All (0, 0, 0) Bed All (0, 0, 0)

In some embodiments, multiple material classifications can have the sametransfer function. For example, for CBCT imaging data, materialclassified as “Soft Tissue” can have the same transfer function asmaterial classified as “Fat.” In another example, material classified as“Bone” can have the same transfer function as material classified as“Dense Bone”

The method can also involve rendering each voxel by applying a transferfunction that corresponds to the material classification correspondingto the voxel (Step 220). The transfer function can receive as input a HUvalue for the respective voxel. Based on the HU value, the transferfunction can output a color (e.g., RGB color) to render the voxel.

FIG. 4 is a flowchart of a method for volume rendering, according tosome embodiments of the invention. Rendering 3D objects can involveidentifying a region of interest and determining which points in thatregion of interest to render. For example, rendering 3D objects caninvolve raycasting. For each frame that is rendered on a 2D screen, intoa virtual reality setting, and/or into an augmenting reality setting,raycasting can be performed. Each time a visualized image is changed(e.g., zoom, rotate, and/or modified), typically multiple new frames canbe determined, and, for each new frame, raycasting can be performed.Current methods for raycasting can be computationally intensive and/orresult in large amounts of data, which can cause rendering of 3D objectsvia raycasting to be prohibitively slow. For example, rendering a 3Dobject of a heart onto a 2D screen, such that a user can rotate theheart, can cause the image of the heart when rotating to appearpixelated and/or cause a user's computer to crash. The method caninvolve raycasting incrementally, which can cause computationalintensity and/or data amount to be reduced.

The method can involve performing a first raycasting on the 3D object toproduce a first intermediary frame, the first raycasting having a firststart position and a first step size (Step 410). The raycasting can havea sampling rate, the step size can be based on the sampling rate. Forexample, if the sampling rate is 10 points per ray, then the step sizecan be 1/10. The 3D object can be described by a volume. The volume canbe a cube that wholly encompasses (or substantially wholly encompasses)the 3D object.

The volume size can depend on a size of the 3D object, resolution of the3D object, or any combination thereof. For example, a pediatric cardiacCT can be physically small, but the volume can be high, due to, forexample, a high resolution scan. In some embodiments, the volume canhave a size of 255×255×300 voxels. In various embodiments, the volume isany volumetric shape as is known in the art.

The first start position can be a first voxel that has data in thevolume that from the viewpoint direction.

The method can involve performing a second raycasting on the 3D objectto produce a second intermediary frame (Step 415). The second raycastingcan include a second start position a second step size. The first startposition and the second start position can be different. The secondstart position can be offset from the first start position. The offsetcan be a randomly generated number, a user input, based a noise functionof a GPU, a constant value, or any combination thereof. In someembodiments, the offset is a random number between 0 and 1. In someembodiments, the offset is checked to ensure that the second startposition is not beyond a predetermined distance from the first startposition.

The first step size and the second step size can be different. Thesecond step size can be offset from the first step size. In someembodiments, the offset is greater than ¼ the first step size.

As shown by step 420, the method can include mixing the firstintermediary frame and the second intermediary frame to render the 3Dobject. Mixing the first intermediary frame and the second intermediaryframe can involve mixing values (e.g., color values) of pixels of thefirst frame and the second frame that are at the same location in theframe.

In some embodiments, mixing values involves taking an average of pixelsof the first intermediary frame and the second intermediary frame thatare at the same location in the frame. In some embodiments, mixingvalues involves taking a weighted average of pixels. For example, ahigher weight can be given to a first frame and a lower weight can begiven to a second, subsequent frame such that the second subsequentframe has less influence on the resulting pixel or frame. In someembodiments, mixing can be done with other functions that are selectedbased on the 3D object data type. For example, if the 3D object datatype is mesh and ray intersection is performed, then a mixing functioncapable of mixing two or more ray intersections can be used.

In some embodiments, the raycasting is performed more than n times,where n is an integer. In some embodiments, n is based on a desiredlevel of detail in the rendered object. In some embodiments, n is aninput. Each time a raycasting is done, the start position and/or thestep size for each raycasting performed can be different or the same asthe previous raycasting operation. In these embodiments, each time araycasting is done, the mixing can involve determining an accumulatedaverage of all raycastings. In some embodiments, each time a ray iscast, detail is added and/or the rendered object will appear richer. Insome embodiments, the number of times the raycasting is performeddepends on a desired level of fidelity for the image.

As described above, current method for volume rendering can beprohibitively slow. One difficulty is that typically during volumerendering all voxels within the volume, whether present or not, arerendered. For example, some parts of a volume can contain or include nocorresponding data. For example, a 3D object of a head can occupy onlypart of a volume having a size of 64×64×256 voxels. Rendering all voxelsin the 64×64×256 volume can be inefficient, since many of the voxels donot have any data that is of interest to rendered (e.g., data outside ofor unrelated to the object). In various embodiments, the volume is anyvolumetric shape as is known in the art.

FIG. 5 a flowchart of a method for volume rendering, according to anillustrative embodiment of the invention. Generally, the method caninvolve creating cubes within a volume, and determining whether any dataexists within each cube (e.g., determining a voxel grid). If a cube isempty the method can involve marking the cube as empty, e.g., byassigning a predefined value to the voxel. If the cube is not empty,e.g., includes data, then the method can involve using the value of thecube for rendering the 3D object to a frame for display on a 2D screen.In this manner, a number of cubes to render can be reduced. In variousembodiments, the cube is any volumetric shape as is known in the art.

The method can involve generating a voxel grid based on the 3D object,each voxel in the voxel grid having a 3D location, size specificationand voxel values (Step 510). Each voxel in the voxel grid can representa center point of a 3D cube volume. Multiple 3D cube volumes can be usedsuch that they fill a volume space.

For example, a volume can have a size of 255×255×300 voxels. Multiple 3Dcubes can be generated within the volume into 3D cubes volumes, each ofthe multiple 3D cubes having a unique 3D location within volume. The 3Dcube volume can have size specification. The size specification can be anumber of voxels to contain within the 3D cube volume or a 3D sizespecification (e.g., A×B×C voxels). For example, the 3D cube volume canhave a size specification of 27 neighbor voxels. In this example, the 3Dcube volume has size of 3×3×3 voxels. In another example, the 3D cubevolume can have a size specification of 4×4×4 voxels. In this example,the 3D cube volume has 64 voxels disposed therein. The sizespecification can be input by a user and/or depend on the object type ofthe 3D object.

The voxel grid can be generated by determining a center point of each 3Dcube volume and assigning that center point to the voxel grid. Forexample, assume a volume that has four 3D cubes and that each 3D cubehas 4 voxels disposed therein. In this example, the volume has 16voxels, and the voxel grid has 4 voxels.

The method also involves for each voxel in the voxel grid: i)determining if the 3D cube volume is empty, and ii) if the 3d cubevolume is empty then assigning an empty value to the current voxel inthe voxel grid, otherwise assign a present value to the current voxel inthe voxel grid (Step 515).

Determining if the 3D cube volume cube volume is empty can involveevaluating the sampled voxels. If the sampled voxels contain values,then it is determined that the 3D cube volume is not empty. If thesampled voxels do not contain values, then it is determined that the 3Dcube volume is empty. In some embodiments, if the values of the sampledvoxels are above a threshold, then it is determined that the 3D cubevolume is not empty, and if they are below a threshold, then it isdetermined that the 3D cube volume is empty.

Processing can decrease dramatically by identifying and ignoring partsof the volume that have little or no data. For example, cubes located inthe space (e.g., air) around a 3D model of a head can be given a valueof zero and can be ignored, thus, drastically decreasing the requiredprocessing.

In some embodiments, a tree structure is created, by setting a size ofcubes (e.g., relative to the size of the 3D object and/or 1/64 cubesizes, 64×64×64), checking input data (e.g. CT data) for each cube, ifthe input data (e.g. the CT data) in the cube doesn't have values biggerthan a threshold, some embodiments can mark the cube as not interesting(e.g., give it a value of zero or any other predefined value thatrepresents no data). Cubes marked as not interesting (e.g., containingno data) can be ignored in further processing, e.g., left out of a treestructure.

If a value greater than a threshold is found in a cube, some embodimentscan mark the cube as interesting (e.g., give it a value of one or anyother predefined value that represents data). Cubes marked asinteresting (e.g., containing data) can be inserted or included in atree structure. In some embodiments, a mesh can be created based on thetree structure, e.g., based on the cubes marked as interesting.

The method can also involve for each cube in a voxel grid having apresent value, rendering the corresponding 3D cube volume based oncorresponding 3D object (Step 520). For example, if a cube in a volumeincludes data (e.g., RGBA values that indicate or correspond to anobject such as bone or blood vessel) then values of a pixel representingthe cube in a 2D frame can be determined based on the data of the cube.In some embodiments, a tree that includes cubes marked as interestingcan be created by a CPU, e.g., by controller 105. In some embodiments, atree can be created by a dedicated hardware unit, e.g., by a graphicsprocessing unit (GPU).

For example, in some embodiments, a GPU can define a voxel grid, e.g.,generate, based on 64×64×64 voxels in a memory of the GPU, a voxel grid,having a cube at each of the points, (each having a 3D position and 3Dsize). It will be noted that implementing the method of FIG. 5 with aGPU can increase speed in comparison with a CPU.

A size of a 3D space over which an embodiment can search for cubes with(and/or without) data as described can be defined by a user. Forexample, rather than a volume of size 64×64×256 as described, any othersize can be selected by a user. Any sampling rate, step or resolutioncan be used, e.g., instead of an 8×8×8 cube used for analyzing cubes ina GPU, a 16×16×16 cube can be used, e.g., in order to increaseperformance.

FIG. 6 shows screenshots of a volume, an optimized tree and a frameaccording to some embodiments of the invention. As shown by screenshot610, a volume can be represented by a single cube. As shown byscreenshot 620, the volume can be broken into smaller cubes. Forexample, instead of using one cube for the whole, or entire, volume,some embodiments can break the volume into smaller cubes, possible withthe same size. The color of cubes can be based on whether or not an areain the volume includes data. Screenshot 630 shows an example of volumerendered created using a tree as described.

As is apparent to one of ordinary skill in the art, the volume renderingcan include any combination of performing the material classification,tree optimization, and incremental raycasting.

In the description and claims of the present application, each of theverbs, “comprise” “include” and “have”, and conjugates thereof, are usedto indicate that the object or objects of the verb are not necessarily acomplete listing of components, elements or parts of the subject orsubjects of the verb. Unless otherwise stated, adjectives such as“substantially” and “about” modifying a condition or relationshipcharacteristic of a feature or features of an embodiment of thedisclosure, are understood to mean that the condition or characteristicis defined to within tolerances that are acceptable for operation of anembodiment as described. In addition, the word “or” is considered to bethe inclusive “or” rather than the exclusive or, and indicates at leastone of, or any combination of items it conjoins.

Descriptions of embodiments of the invention in the present applicationare provided by way of example and are not intended to limit the scopeof the invention. The described embodiments comprise different features,not all of which are required in all embodiments. Some embodimentsutilize only some of the features or possible combinations of thefeatures. Variations of embodiments of the invention that are described,and embodiments comprising different combinations of features noted inthe described embodiments, will occur to a person having ordinary skillin the art. The scope of the invention is limited only by the claims.

Unless explicitly stated, the method embodiments described herein arenot constrained to a particular order in time or chronological sequence.Additionally, some of the described method elements can be skipped, orthey can be repeated, during a sequence of operations of a method.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents can occur to those skilled in the art. It is, therefore, tobe understood that the appended claims are intended to cover all suchmodifications and changes as fall within the true spirit of theinvention.

Various embodiments have been presented. Each of these embodiments canof course include features from other embodiments presented, andembodiments not specifically described can include various featuresdescribed herein.

1. A method for volume rendering three-dimensional (3D) image data, themethod comprising: for each voxel in the 3D imaging data, determining amaterial classification; for each material classification determine acorresponding transfer function; and rendering each voxel in the 3Dimaging data based on a transfer function that corresponds to thematerial classification corresponding to the voxel.
 2. The method ofclaim 1 wherein determining the material classification furthercomprises: determining an initial material classification; segmentingthe 3D imaging data; and determining the material classification basedon the initial material classification and the segmented 3D imagingdata.
 3. The method of claim 2 wherein determining an initial materialclassification value is based on a HU value of the respective voxel. 4.The method of claim 2 wherein determining an initial materialclassification value is based on a probability map.
 5. The method ofclaim 2 wherein the segmenting is based on a magnitude of a gradient ofeach voxel.
 6. The method of claim 2 wherein segmenting the 3D imagingdata further comprises dilating, eroding, opening or closing all or aportion of the 3D imaging data.
 7. The method of claim 2 whereindetermining the material classification further comprises determining anintersection between the segmented 3D imaging data.
 8. The method ofclaim 1 wherein determining the corresponding transfer function isfurther based on a HU value.
 9. A non-transient computer readable mediumcontaining program instructions for causing a computer to perform themethod of: for each voxel in the 3D imaging data, determining a materialclassification; for each material classification determine acorresponding transfer function; and rendering each voxel in the 3Dimaging data based on a transfer function that corresponds to thematerial classification corresponding to the voxel.
 10. A method forvolume rendering a three-dimensional (“3D”) object, the methodcomprising: performing a first raycasting on the 3D object to produce afirst intermediary frame, the first raycasting having a first startposition and a first step size; performing a second raycasting on the 3Dobject to produce a second intermediary frame, the second raycastinghaving a second start position a second step size, wherein the firststart position and the second start position are different and whereinthe first step size and a second step size are different; and mixing thefirst intermediary frame and the second intermediary frame to render the3D object.
 11. The method of claim 10 wherein the first step size isbased on a sampling rate of the raycasting.
 12. The method of claim 10wherein the second step size is based on the first step size and anoffset.
 13. The method of claim 10 wherein mixing further comprises: foreach pixel in the first intermediary frame and the second intermediaryframe at a pixel location that is the same, mixing the firstintermediary frame values and the second intermediary frame values atthe pixel location to determine final pixel values at the pixellocation.
 14. The method of claim 10 wherein mixing the firstintermediary frame values and the second intermediary frame values atthe pixel location further comprises averaging the first intermediaryframe values and the second intermediary frame values, performing aweighted averaging of the first intermediary frame values and the secondintermediary frame values, accumulated averaging, or any combinationthereof.
 15. The method of claim 10 wherein the second start position isthe first start position with an offset value.
 16. The method of claim15 where the offset value is randomly generated, input by a user, or anycombination thereof.
 17. A non-transient computer readable mediumcontaining program instructions for causing a computer to perform themethod of: performing a first raycasting on the 3D object to produce afirst intermediary frame, the first raycasting having a first startposition and a first step size; performing a second raycasting on the 3Dobject to produce a second intermediary frame, the second raycastinghaving a second start position a second step size, wherein the firststart position and the second start position are different and whereinthe first step size and the second step size are different; and mixingthe first intermediary frame and the second intermediary frame to renderthe 3D object.
 18. A method for volume rendering three-dimensional (3D)image data, the method comprising: generating a voxel grid based on the3D object, each voxel in the voxel grid having a three dimensionallocation, a size specification and voxel values and each voxel in thevoxel grid represents a center point of a 3D cube volume having therespective size specification; for each voxel in the voxel grid: i)determine if the 3D cube volume is empty, and ii) if the 3D cube volumeis empty assign an empty value to the current voxel in the voxel grid,otherwise assign a present value to the current voxel in the voxel grid;and for each voxel in the voxel grid having a present value, render thecorresponding 3D cube volume based on the corresponding 3D object to aframe for display on the 2D screen.
 19. The method of claim 18 whereinthe size specification is input by a user, based on a type of the 3Dobject, size of the 3D object or any combination thereof.
 20. The methodof claim 18 further comprising rendering the voxel grid based on thepresent and empty values to a frame for display on the 2D screen. 21.The method of claim 18 wherein the rendering is performed on a graphicalprocessing unit.
 22. A non-transient computer readable medium containingprogram instructions for causing a computer to perform the method of:generating a voxel grid based on the 3D object, each voxel in the voxelgrid having a three dimensional location, a size specification and voxelvalues and each voxel in the voxel grid represents a center point of a3D cube volume having the respective size specification; for each voxelin the voxel grid: iii) determine if the 3D cube volume is empty, andiv) if the 3D cube volume is empty assign an empty value to the currentvoxel in the voxel grid, otherwise assign a present value to the currentvoxel in the voxel grid; and for each voxel in the voxel grid having apresent value, render the corresponding 3D cube volume based on thecorresponding 3D object to a frame for display on the 2D screen.